k_bbq_train.m

function model = k_bbq_train(X,Y,model)
% K_BBQ_TRAIN Kernel Bound on Bias Query Algorithm
%
%    MODEL = K_ BBQ_TRAIN(X,Y,MODEL) trains an classifier according to the
%    Bound on Bias Query Algorithm, with kernels. The algorithm will query
%    a label only on certain rounds.
%
%    Additional parameters:
%    - model.k is exponent of the query rate.
%      Default value is 1/2.
%
%   References:
%     - Orabona, F., Cesa-Bianchi, N. (2011).
%       Better Selective Sampling Algorithms.
%       Proceedings of the 26th International Conference on Machine Learning.
%
%     - Cesa-Bianchi, N., Gentile, C., & Orabona, F. (2009)
%       Robust Bounds for Classification via Selective Sampling.
%       Proceedings of the 26th International Conference on Machine
%       Learning.

%    This file is part of the DOGMA library for MATLAB.
%    Copyright (C) 2009-2011, Francesco Orabona
%
%    This program is free software: you can redistribute it and/or modify
%    it under the terms of the GNU General Public License as published by
%    the Free Software Foundation, either version 3 of the License, or
%    (at your option) any later version.
%
%    This program is distributed in the hope that it will be useful,
%    but WITHOUT ANY WARRANTY; without even the implied warranty of
%    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
%    GNU General Public License for more details.
%
%    You should have received a copy of the GNU General Public License
%    along with this program.  If not, see <http://www.gnu.org/licenses/>.
%
%    Contact the author: francesco [at] orabona.com

n = length(Y);   % number of training samples

if isfield(model,'iter')==0
    model.iter = 0;
    model.beta = [];
    model.beta2 = [];
    model.errTot = 0;
    model.numSV = zeros(numel(Y),1);
    model.aer = zeros(numel(Y),1);
    model.pred = zeros(numel(Y),1);

    model.Kinv = 0;
    model.Y_S = [];
    model.N = 0;
    model.numQueries = 0;
    model.nacr = zeros(numel(Y),1);
end

if isfield(model,'k')==0
    model.k = 1/2;
end

for i = 1:n
    model.iter = model.iter+1;
        
    if numel(model.S)>0
        if isempty(model.ker)
            K_f = X(model.S,i);
            Kii = X(i,i);
        else
            K_f = feval(model.ker,model.SV,X(:,i),model.kerparam);
            Kii = feval(model.ker,X(:,i),X(:,i),model.kerparam);
        end
        val_f = model.beta*K_f;
    else
        if isempty(model.ker)
            Kii = X(i,i);
        else
            Kii = feval(model.ker,X(:,i),X(:,i),model.kerparam);
        end
        val_f = 0;
        K_f = 0;
    end

    Yi = Y(i);
    
    model.errTot = model.errTot+(sign(val_f)~=Yi);
    model.aer(model.iter) = model.errTot/model.iter;
    model.nacr(model.iter) = (model.iter-model.errTot)/model.numQueries;
    
    coeff = K_f'*model.Kinv;
    delta = Kii-coeff*K_f;
    
    val_f = val_f/(delta+1);
    model.pred(model.iter) = val_f;
    rt = delta/(delta+1);
    
    if rt>0.5*model.iter^(-model.k)
        model.numQueries = model.numQueries+1;
        model.S(end+1) = model.iter;
        if ~isempty(model.ker)
            model.SV(:,end+1) = X(:,i);
        end
        model.Y_S(end+1) = Yi;

        if numel(model.S)>1
            tmp = [model.Kinv, zeros(numel(model.S)-1,1);zeros(1,numel(model.S))];
            tmp = tmp+[coeff'; -1]*[coeff'; -1]'/(delta+1);
        else
            tmp = full((Kii+1)^-1);
        end
        model.Kinv = tmp;

        model.beta = model.Y_S*model.Kinv;
        model.N = model.N+1;
    end
    
    model.numSV(model.iter) = numel(model.S);

    if mod(i,model.step)==0
      fprintf('#%.0f SV:%5.2f(%d)\tAER:%5.2f\tQueried Labels:%5.2f(%d)\n', ...
            ceil(i/1000),numel(model.S)/model.iter*100,numel(model.S),...
            model.aer(model.iter)*100,model.numQueries/model.iter*100,...
            model.numQueries);
    end
end